continued fraction

American  

noun

Mathematics.

1. a fraction whose denominator contains a fraction whose denominator contains a fraction, and so on.

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continued fraction British  

noun

1. a number plus a fraction whose denominator contains a number and a fraction whose denominator contains a number and a fraction, and so on

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Etymology

Origin of continued fraction

First recorded in 1860–65

Example Sentences

See Examples For:

continued fraction

These latest projects are primarily driven by a specific continued fraction whose nested integers form the sequence 1, 2, 3,…, Elsner says.

From Scientific American ● Jun. 2, 2023

If b2/a2, b3/a3 ..., the component fractions, as they are called, recur, either from the commencement or from some fixed term, the continued fraction is said to be recurring or periodic.

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

The Incommensurability of Infinite Continued Fractions.—There is no general test for the incommensurability of the general infinite continued fraction.

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

Any exact fraction can be expressed as a continued fraction, and there are methods for expressing as continued fractions certain other numbers, e.g. square roots, whose values cannot be expressed exactly as fractions.

From Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" by Various

If a or b is unity, a/b cannot be converted into a continued fraction with unit numerators, and the above method fails.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" by Various